Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)

Abstract We derive Euler–Lagrange‐type equations for fractional action‐like integrals of the calculus of variations which depend on the Riemann–Liouville derivatives of order (α, β), α>0, β>0, recently introduced by Cresson. Some interesting consequences are obtained and discussed. Copyright © 2007 John Wiley & Sons, Ltd.